A226119 Numbers such that sigma(phi(tau(n)))=tau(phi(sigma(n))).

1, 6, 36, 64, 105, 114, 135, 1980, 2016, 3072, 5120, 7056, 7840, 9216, 16320, 18720, 18900, 23100, 23622, 24003, 25536, 26088, 26733, 28455, 29078, 29337, 29700, 29760, 30597, 30894, 30912, 31155, 31496, 31758, 32361, 33782, 34020, 34286, 36000, 36036, 36099

Offset: 1

Author

Paolo P. Lava, May 27 2013

Keywords

• nonn

Examples

			29337 is in the sequence since:
sigma(29337)=49152 -> phi(49152)=16384 -> tau(16384)=15.
tau(29337)=16 -> phi(16)=8 -> sigma(8)=15.
		

Links

• Paolo P. Lava and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 270 terms from Paolo P. Lava)

Crossrefs

Cf. A000005, A000010, A000203, A033632, A067160, A076361, A226117, A226118.

Programs

Maple

with(numtheory); A226119:=proc(q) local n;
for n from 1 to q do
if sigma(phi(tau(n)))=tau(phi(sigma(n))) then print(n);
fi; od; end: A226119(10^6);

Mathematica

Select[Range[36099], DivisorSigma[1, EulerPhi[DivisorSigma[0, #]]] == DivisorSigma[0, EulerPhi[DivisorSigma[1, #]]] &] (* T. D. Noe, May 28 2013 *)